Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions

在线阅读 下载PDF 导出详情
摘要 Inthispaperwefirstconsiderariskprocessinwhichclaiminter-arrivaltimesandthetimeuntilthefirstclaimhaveanErlang(2)distribution.Anexplicitsolutionisderivedfortheprobabilityofultimateruin,givenaninitialreserveofuwhentheclaimsizefollowsaParetodistribution.FollowRamsay,Laplacetransformsandexponentialintegralsareusedtoderivethesolution,whichinvolvesasingleintegralofrealvaluedfunctionsalongthepositiverealline,andtheintegrandisnotofanoscillatingkind.ThenweshowthattheultimateruinprobabilitycanbeexpressedasthesumofexpectedvaluesoffunctionsoftwodifferentGammarandomvariables.Finally,theresultsareextendedtotheErlang(n)case.Numericalexamplesaregiventoillustratethemainresults.
机构地区 不详
出版日期 2004年03月13日(中国期刊网平台首次上网日期,不代表论文的发表时间)